The poem is about a long, dreary, monotonous prison sentence for a nameless prisoner. The story gets more exciting than this (his two brothers die! a bird comes to cheer him up!), but the basic story is about the passage of a long, weary, lonely time in prison. The sound of the poem reflects this pretty well: the repeated rhythm (iambic tetrameter – check out the "Form and Meter" section for more on that) is like the steady rhythm of the waves of the lake that the speaker says he can hear, night and day, from his dungeon. The repetition of the rhyming words at the end of each line also adds to the sense of a long, monotonous period of time. Byron often repeats the same sentence structure, too – check out lines 36-37:
And in each pillar there is a ring,
And in each ring there is a chain;
Or, check out lines 240-241:
It was not night, it was not day;
It was not even the dungeon-light,
If that's not enough repetition for you, just think about the plot of the poem. First one brother dies and is buried in the dungeon, then the second brother dies and is likewise buried in the floor of the dungeon.
All this repetition adds up to one thing: the sound of the poem (on multiple levels) reflects, in just 392 lines, the sense that the prisoner has been in prison for a looooooong and dreary time.